The graph of y = f (x) = b^x, where b > 1, is translated such that the equation of
the new graph is expressed as
y – 2 = f (x – 1). The range of the new function is
A. y > 2
B. y > 3
C. y > –1
D. y > –2
2)If log7 m = log 2/3 , then the value of m, correct to the nearest hundredth
i am really confused in these questions..help please!
thank u in advance
the graph of y = b^x , b > 0, has the x-axis as a horizontal asymptote and its range is y > 0
rewriting your function
as
y = f (x – 1) + 2
we can see that the new function has been moved UP two units, so its range is
y > 2
By log7 m = log 2/3
do you mean
log 7 m = log (2/3).
I will wait til your clarify?
Hi,
for question 1, I got y>2 as well but the answer is y>3 in my book.
and yes for question 2
trust yourself, you have "raised" the graph of the function by 2
2.
general rule: log ab = log b/log a
so log m/log 7 = log2 - log3
log m = log7(log2-log3)
log m = -.1488
m = 10^-.1488
m = .70988
thank u =)
1) To determine the range of the new function, we need to understand how the translation and transformation affect the original function.
The given equation is y - 2 = f(x - 1), which means the graph is translated one unit to the right and two units upward.
For the original function y = b^x, where b > 1, the range is y > 0. This is because as x approaches negative infinity, the value of the exponent b^x approaches zero, and as x approaches positive infinity, the value of the exponent approaches infinity.
When the original graph is translated one unit to the right (x - 1), it does not affect the range.
However, when the graph is translated two units upward (y - 2), it shifts the entire range upward by two units. Therefore, the range of the new function is y > 2.
So, the answer is A. y > 2.
2) To solve the equation log7 m = log 2/3, we can use the property of logarithms which states that if log a x = log a y, then x = y.
In this case, we have log7 m = log 2/3. We can rewrite log 2/3 as log(2/3)/log(10) to convert it to a common logarithm.
log7 m = log(2/3)/log(10)
Now, we can use the property mentioned above:
m = 2/3
Therefore, the value of m is 2/3, correct to the nearest hundredth.
So, the answer is m ≈ 0.67.
I hope that helps! Let me know if you have any further questions.